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$\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \cdots + \frac{1}{k^2} \leq 2 - \frac{1}{k} .$



$\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \cdots + \frac{1}{k^2} + \frac{1}{(k+1)^2}\leq 2 - \frac{1}{k} + \frac{1}{(k+1)^2} $

$\sum_{i=1}^k+1 \frac{1}{i^[2]} \leq 2 - \frac{1}{k} + \frac{1 ...